Preheat the oven to 375 degrees F (190 degrees C).
Combine graham cracker crumbs, sugar, and melted butter for crust in a bowl until well mixed. Press into the bottom and halfway up the sides of a 9-inch round pan.
Combine cream cheese, sugar, eggs, and vanilla extract for filling in a large bowl; beat with an electric mixer until smooth and creamy, 2 to 3 minutes. Pour into crust.
Bake in the preheated oven until nearly set and only slightly jiggly in the center, about 18 minutes. Raise the oven temperature to 475 degrees F (245 degrees C) and keep cheesecake in for 2 minutes. Remove from the oven and cool on a wire rack for 15 minutes. Leave the oven on.
Combine sour cream, sugar, and vanilla extract in a bowl and mix with a spoon. Pour carefully over the cooled filling.
Bake in the oven until topping is set, about 10 minutes. Remove from the oven and let stand at room temperature for 5 to 6 hours. Refrigerate until ready to serve.